ML/Google Distinguished Lecture Series-Machine Learning Department - Carnegie Mellon University

Machine Learning Special Seminars

Spring 2017 Seminar
Date: February 7, 2017
Time: 4:30 PM - 5:30 PM
Location: 6115 Gates and Hillman Centers
Speaker: Bharath Sriperumbudur Assistant Professor, Penn State
Title: Shrinkage Estimation in Reproducing Kernel Hilbert Spaces
Abstract: Over the last few years, kernel embedding of distributions has gained a lot of attention in the machine learning community due to the wide variety of applications it has been employed in. Some of these applications include kernel-based non-parametric hypothesis tests, covariate-shift, density estimation, feature selection, causal inference and distribution regression. All these applications require an estimate of the kernel mean based on random samples drawn i.i.d. from an unknown distribution. Usually, an empirical estimator of the kernel mean is employed in these applications. In this talk, we propose alternative estimators of the kernel mean based on the idea of shrinkage estimation. Motivated by the classical James-Stein shrinkage for the estimation of a mean vector of a Gaussian distribution on R^d, we propose non-parametric shrinkage estimators in RKHS and establish consistency and oracle inequalities. We will establish a connection between shrinkage estimation and regularization in RKHS and through numerical experiments, we highlight the importance of these shrinkage estimators in small sample, high dimensional settings.
Speaker Bio: Bharath Sriperumbudur is an Assistant Professor in the Department of Statistics at Pennsylvania State University. His research interests include nonparametric statistics, machine learning, regularization and inverse problems, reproducing kernel spaces in probability and statistics and statistical learning theory.